Problem: Solve for $x$ and $y$ using elimination. ${3x-3y = -18}$ ${-4x-2y = -36}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $-3$ ${6x-6y = -36}$ $12x+6y = 108$ Add the top and bottom equations together. $18x = 72$ $\dfrac{18x}{{18}} = \dfrac{72}{{18}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {3x-3y = -18}\thinspace$ to find $y$ ${3}{(4)}{ - 3y = -18}$ $12-3y = -18$ $12{-12} - 3y = -18{-12}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 4}$ into $\thinspace {-4x-2y = -36}\thinspace$ and get the same answer for $y$ : ${-4}{(4)}{ - 2y = -36}$ ${y = 10}$